Problem: William decided to paint some of the rooms at his 7-room inn, William's Place. He discovered he needed $\frac{4}{5}$ of a can of paint per room. If William had 4 cans of paint, how many rooms could he paint?
We can divide the cans of paint (4) by the paint needed per room ( $\frac{4}{5}$ of a can) to find out how many rooms William could paint. $ \dfrac{{4 \text{ cans of paint}}} {{\dfrac{4}{5} \text{ can per room}}} = {\text{ rooms}} $ Dividing by a fraction is the same as multiplying by the reciprocal. The reciprocal of ${\dfrac{4}{5} \text{ can per room}}$ is ${\dfrac{5}{4} \text{ rooms per can}}$ $ {4\text{ cans of paint}} \times {\dfrac{5}{4} \text{ rooms per can}} = {\text{ rooms}} $ ${\dfrac{20}{4}\text{ rooms}} = 5\text{ rooms}$ William could paint 5 rooms.